Lapping is a well established process for finishing the tooth surfaces of bevel gears. It is a process that provides an economical alternative to other hard finishing processes for bevel gears.
In the lapping process, a pinion and ring gear are mounted, via appropriate workholding equipment, to respective spindles in a lapping machine which has the same basic design as a testing machine. In most instances of rolling of the gear set, the pinion is the driving member and the ring gear is braked. The gears are rolled in mesh and lapping compound, which can be a mixture of oil (or water) and silicon carbide or similar abrasive, is poured into the meshing zone. An example of lapping and/or testing machines can be found in U.S. Pat. No. 6,120,355 to Stadtfeld et al.
Most lapping and testing machines have three degrees of freedom available for realizing relative motion between a ring gear and pinion. The first freedom being relative movement in the direction of the ring rear axis (gear cone distance) which shall be referred to as direction G or the G-axis, the second freedom being relative movement in direction of the pinion axis (pinion cone distance) which shall be referred to as direction P or the P-axis, and the third degree of freedom being distance between the ring gear and pinion axes which shall be referred to as direction E or the E-axis. The direction E is also known as the “hypoid offset” or “pinion offset.”
In lapping or testing processes, relative movement in the E, P and G directions effect positional changes in the contact pattern of the members of the gear set, in effect modifying the contact pattern. Lapping involves rotating the gear members in mesh with contact at a desired position on the tooth surfaces. Thus, the members are located at particular E and P positions along with a particular G-axis position to effect the desired backlash.
Typically, the E, P and G movements each have an effect on both the lengthwise and depthwise position of the localized tooth contact pattern, the primary effect of the E-axis movement being on the relative lengthwise position of the contact pattern, the primary effect of P-axis movement being on the relative depthwise position of the contact pattern, and the primary effect of G-axis movement being on the backlash.
As the gear set is lapped, contact is usually shifted from the center of the tooth toward one of the outer (heel) or inner (toe) portions of the tooth surface by changing the E and P settings as necessary to effect such a shifting of the contact position. As E and P are changed to effect the shifting, the G-axis position must also be changed to maintain the desired backlash. When the desired heel or toe position is reached, E and P axes positions are again changed to shift contact to the other of the heel or toe positions with the changing E and P positions being accompanied by an appropriate G-axis change to maintain backlash. The contact position is then returned to the beginning position at the center of the tooth. Lapping carried out by shifting of contact from heel-center-toe (or toe-center-heel) along the tooth length as described above may be referred to as “3 point sweep lapping.”
Material removal is different in different areas or “zones” of a tooth flank surface depending on local sliding velocities, normal forces as well as hydrodynamic effects which support or prevent the sufficient access of lapping compound between the flanks in the contacting zone. The material removed on the pinion member is also different than the amount of material removal on the ring gear flank surfaces. One reason for this is the usual lower number of teeth on a pinion results in more pinion revolutions per unit of time than ring gear revolutions. Another reason is the different surface curvature and velocity direction of a pinion versus a ring gear results in different trends in material removal.
The consolidation of different effects and dependencies leads to a complex higher order relationship between lapping parameters and the amount of material removed on the tooth flank surfaces. Lapping part programs in modern lapping machines, such as the type disclosed in U.S. Pat. No. 6,120,355, normally use three target points (at heel, center and toe) to move the contact zone in a slow motion between those three points (while the axis rotates at up to 2000 RPM or more). In general the pinion drives the ring gear which provides some resistance with a rather low torque usually between 3 and 30 Nm. The pinion changes the direction of rotation to lap the opposite flanks (e.g. starting with coast side lapping followed by drive side lapping). The sequence of coast side lapping and drive side lapping is preferably repeated several times to complete a lapping cycle. The gear torque can also be changed from resisting the pinion rotation to the same direction of the pinion rotation in order to lap the opposite flanks. The combination of two directions of rotation and two directions of torque application enable a so-called “four quadrant” operation.
Developing a lapping program for a certain gear design requires a significant practical experience since the influence of a lapping process on a flank surface is complex and usually difficult to control. There are no theoretical aids that can help to reliably predict the influence of lapping on the tooth contact pattern, the motion transmission error or the flank form.
As a result, there are no coordinate measurements conducted subsequent to lapping to detect and improve the flank surface versus a nominal flank form. The most common measurements after lapping are roll tests which show the tooth contact under light load and the transmission quality. However, if, for example, the transmission error is too large or the contact pattern has the wrong position within the boundaries of the teeth, it is not possible to calculate changes to the lapping process in order to achieve the desired results. Presently, corrections to the lapping process are made intuitively and/or by trial and error.